A050123 a(n) = b(n)-b(n-1), where b=A050122 (ordered products of Fibonacci and Lucas numbers).

1, 2, 1, 3, 1, 3, 3, 4, 3, 1, 7, 4, 3, 11, 7, 1, 3, 18, 11, 3, 4, 29, 18, 3, 1, 7, 47, 29, 4, 3, 11, 76, 47, 7, 1, 3, 18, 123, 76, 11, 3, 4, 29, 199, 123, 18, 3, 1, 7, 47, 322, 199, 29, 4, 3, 11, 76